Discrete Data Sets Research Articles

Identification of affine dynamical systems from a single trajectory

For dynamical systems of the form ẋ = Ax + c, henceforth called affine systems, we study the problem of determining system parameters A, c from data derived from a single trajectory. We establish necessary and sufficient conditions for identifiability of parameters from either a full trajectory or a set of discrete data points sampled from a single trajectory, expressed as geometrical conditions on the trajectory. We describe conditions under which the system has an equilibrium point and examine the problem of identifiability of the equilibrium point from data. We briefly examine the analytical upper and lower bounds for the maximal permissible uncertainty that will guarantee an inverse with specified qualitative properties of the resulting system (e.g., stability, spirality, and so on). Finally, we illustrate an application of the theory to parameter estimation for a class of nonlinear systems consisting of linear-in-parameters systems and demonstrate that affine approximations can yield more accurate estimates of parameter values than those based on finite differences.

Uma proposta de orientação para o uso de modelos contínuos em dados de sobrevivência discretos

Modelos discretos não são populares em análise de sobrevivência. Isso se deve principalmente à escassez de trabalhos que abordam a análise de dados discretos na presença de censura. Desta forma, a possibilidade de analisar um conjunto de dados discretos por meio de um modelo contínuo certamente traz facilidade à análise desses dados. Neste contexto, este trabalho propõe guias de decisão que podem auxiliar um pesquisador decidir sobre o uso de um modelo contínuo na análise de dados de sobrevivência originalmente discretos. Esses guias de decisão foram obtidos por meio de simulações de Monte Carlo e levam em consideração o tamanho da amostra, o percentual de censura e a proporção de observações empatadas. Os guias de decisão foram aplicados em três conjuntos de dados obtidos na literatura e se mostrou uma forma simples de decidir quando um modelo contínuo pode ser considerado para o ajuste de dados discretos.

Building General Langevin Models from Discrete Datasets

Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in the quantitative reconstruction of the model from experimental data, even in the simple case of equilibrium Langevin dynamics of Hamiltonian systems. We develop a novel Bayesian inference approach to learn the parameters of such stochastic effective models from discrete finite length trajectories. We first discuss the failure of naive inference approaches based on the estimation of derivatives through finite differences, regardless of the time resolution and the length of the sampled trajectories. We then derive, adopting higher order discretization schemes, maximum likelihood estimators for the model parameters that provide excellent results even with moderately long trajectories. We apply our method to second order models of collective motion and show that our results also hold in the presence of interactions.

A new data-driven topology optimization framework for structural optimization

The application of structural topology optimization with complex engineering materials is largely hindered due to the complexity in phenomenological or physical constitutive modeling from experimental or computational material data sets. In this paper, we propose a new data-driven topology optimization (DDTO) framework to break through the limitation with the direct usage of discrete material data sets in lieu of constitutive models to describe the material behaviors. This new DDTO framework employs the recently developed data-driven computational mechanics for structural analysis which integrates prescribed material data sets into the computational formulations. Sensitivity analysis is formulated by applying the adjoint method where the tangent modulus of prescribed uniaxial stress-strain data is evaluated by means of moving least square approximation. The validity of the proposed framework is well demonstrated by the truss topology optimization examples. The proposed DDTO framework will provide a great flexibility in structural design for real applications.

Two Optimal Measurements of Normality for Finite Set of Discrete Data

When one applies statistical models, he usually makes the assumption that the data or error come from a normal distribution. In order to verify or to estimate the parameters of the normal distribution, the typical approaches would be normality tests and model selections. In this article, we come up with two methods that could fit the data via normal distribution and measure the fitness. This would serve an alternative for model selection. Unlike statistical approaches - parametric or non-parametric statistics - we use approximation approaches to measure the optimal similarity between a given data set and its induced normal distributions and then search for the optimal normal distribution that has the best similarities. The degree of similarity is defined by two approaches: the overlapped area and the arccos function. The idea is to look at the patterns between data set induced step function and sampled normal distributions in the form of approximated step probability density functions. Our analytical approach could measure the degree of normality, or the similarity with normal distributions, which could then used in pioneering findings for related statistical inferences

A systematic framework for formulating convex failure envelopes in multiple loading dimensions

The failure envelope approach is widely used to assess the ultimate capacity of shallow foundations for combined loading, and to develop foundation macro-element models. Failure envelopes are typically determined by fitting appropriate functions to a set of discrete failure load data, determined either experimentally or numerically. However, current procedures to formulate failure envelopes tend to be ad hoc, and the resulting failure envelopes may not have the desirable features of being convex and well-behaved for the entire domain of interest. This paper describes a new systematic framework to determine failure envelopes – based on the use of sum of squares convex polynomials – that are guaranteed to be convex and well-behaved. The framework is demonstrated by applying it to three data sets for failure load combinations (vertical load, horizontal load and moment) for shallow foundations on clay. An example foundation macro-element model based on the proposed framework is also described.

Working Towards the Australian National Quality Standard for ECEC: what do we know? Where should we go?

The most recent data from the Australian Children’s Education and Care Quality Authority (ACECQA) present good news; 79% of Australia’s Early Childhood Education and Care services are now meeting the National Quality Standard (NQS). Yet one in five services remain below standard. Understanding the context and characteristics of these services, and those of their workforce, and identifying features that distinguish them from services meeting the NQS are the first step in directing quality improvement supports. We compared services rated Working Towards with those Meeting or Exceeding the standard, through analysis of two discrete datasets: (1) ACECQA snapshots providing service data and (2) The Early Years Workforce Study providing data on educators and educator experience. We identified distinguishing structural characteristics and relational factors within services rated Working Towards. Based on the findings, strategic directions for bringing the last 21% of services across the line to meet the National Quality Standard are detailed.

Mathematical approach to the validation of field surface texture parameter software

A new method for performance validation of surface texture parameter calculation software is introduced, focussing on field surface texture parameters. Surface height functions are defined mathematically, either using Fourier series or polynomials, and are then input into the surface texture parameter definitions to obtain mathematical parameter values. A series of user-adjustable parametric surface functions are defined that correspond to each surface texture parameter, enabling users to create a variety of surfaces to assess their software whilst still retaining mathematical traceability. This method is expanded to include complex surface textures. Chebyshev polynomials are used to perform numerical calculations of surface texture parameters for a selection of polynomial surface functions. Mathematical reference parameter values are calculated for a series of fifteen predefined surfaces and ten parametric surfaces to assess the performance of the software under test for a given dataset resolution. Assessment of the number of significant figures of the software-obtained values that agree with the reference values is used as a performance metric that enables comparison between different third-party software applications for a given dataset resolution. An assessment of the sampling methods used to create discrete datasets of a mathematical surface function for use with numerical third-party software is performed. Two implementations of surface height sampling are used to create datasets that are input into four third-party surface texture parameter calculation software packages, and the results compared, showing a significant variation in the performance metric values for different sampling methods.

Forecasting the movements of Bitcoin prices: an application of machine learning algorithms

Cryptocurrencies, such as Bitcoin, are one of the most controversial and complex technological innovations in today's financial system. This study aims to forecast the movements of Bitcoin prices at a high degree of accuracy. To this aim, four different Machine Learning (ML) algorithms are applied, namely, the Support Vector Machines (SVM), the Artificial Neural Network (ANN), the Naive Bayes (NB) and the Random Forest (RF) besides the logistic regression (LR) as a benchmark model. In order to test these algorithms, besides existing continuous dataset, discrete dataset was also created and used. For the evaluations of algorithm performances, the F statistic, accuracy statistic, the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE) and the Root Absolute Error (RAE) metrics were used. The t test was used to compare the performances of the SVM, ANN, NB and RF with the performance of the LR. Empirical findings reveal that, while the RF has the highest forecasting performance in the continuous dataset, the NB has the lowest. On the other hand, while the ANN has the highest and the NB the lowest performance in the discrete dataset. Furthermore, the discrete dataset improves the overall forecasting performance in all algorithms (models) estimated.

Piecewise Linear Function Fitting via Mixed-Integer Linear Programming

Piecewise linear (PWL) functions are used in a variety of applications. Computing such continuous PWL functions, however, is a challenging task. Software packages and the literature on PWL function fitting are dominated by heuristic methods. This is true for both fitting discrete data points and continuous univariate functions. The only exact methods rely on nonconvex model formulations. Exact methods compute continuous PWL function for a fixed number of breakpoints minimizing some distance function between the original function and the PWL function. An optimal PWL function can only be computed if the breakpoints are allowed to be placed freely and are not fixed to a set of candidate breakpoints. In this paper, we propose the first convex model for optimal continuous univariate PWL function fitting. Dependent on the metrics chosen, the resulting formulations are either mixed-integer linear programming or mixed-integer quadratic programming problems. These models yield optimal continuous PWL functions for a set of discrete data. On the basis of these convex formulations, we further develop an exact algorithm to fit continuous univariate functions. Computational results for benchmark instances from the literature demonstrate the superiority of the proposed convex models compared with state-of-the-art nonconvex models.

Decision Tree-Based Data Mining and Rule Induction for Identifying High Quality Groundwater Zones to Water Supply Management: a Novel Hybrid Use of Data Mining and GIS

Groundwater is an important source to supply drinking water demands in both arid and semi-arid regions. Nevertheless, locating high quality drinking water is a major challenge in such areas. Against this background, this study proceeds to utilize and compare five decision tree-based data mining algorithms including Ordinary Decision Tree (ODT), Random Forest (RF), Random Tree (RT), Chi-square Automatic Interaction Detector (CHAID), and Iterative Dichotomiser 3 (ID3) for rule induction in order to identify high quality groundwater zones for drinking purposes. The proposed methodology works by initially extracting key relevant variables affecting water quality (electrical conductivity, pH, hardness and chloride) out of a total of eight existing parameters, and using them as inputs for the rule induction process. The algorithms were evaluated with reference to both continuous and discrete datasets. The findings were speculative of the superiority, performance-wise, of rule induction using the continuous dataset as opposed to the discrete dataset. Based on validation results, in continuous dataset, RF and ODT showed higher and RT showed acceptable performance. The groundwater quality maps were generated by combining the effective parameters distribution maps using inducted rules from RF, ODT, and RT, in GIS environment. A quick glance at the generated maps reveals a drop in the quality of groundwater from south to north as well as from east to west in the study area. The RF showed the highest performance (accuracy of 97.10%) among its counterparts; and so the generated map based on rules inducted from RF is more reliable. The RF and ODT methods are more suitable in the case of continuous dataset and can be applied for rule induction to determine water quality with higher accuracy compared to other tested algorithms.

A New Heuristic Approach for Treating Missing Value: ABCimp

Missing values in datasets present an important problem for traditional and modern statistical methods. Many statistical methods have been developed to analyze the complete datasets. However, most of the real world datasets contain missing values. Therefore, in recent years, many methods have been developed to overcome the missing value problem. Heuristic methods have become popular in this field due to their superior performance in many other optimization problems. This paper introduces an Artificial Bee Colony algorithm based new approach for missing value imputation in the four real-world discrete datasets. At the proposed Artificial Bee Colony Imputation (ABCimp) method, Bayesian Optimization is integrated into the Artificial Bee Colony algorithm. The performance of the proposed technique is compared with other well-known six methods, which are Mean, Median, k Nearest Neighbor (k-NN), Multivariate Equation by Chained Equation (MICE), Singular Value Decomposition (SVD), and MissForest (MF). The classification error and root mean square error are used as the evaluation criteria of the imputation methods performance and the Naive Bayes algorithm is used as the classifier. The empirical results show that state-of-the-art ABCimp performs better than the other most popular imputation methods at the variable missing rates ranging from 3 % to 15 %.

Data-driven approach to characterize urban vitality: how spatiotemporal context dynamically defines Seoul’s nighttime

ABSTRACTThis study takes a data-driven approach to define urban nighttime by examining the spatiotemporal dynamics of urban vitality. Using micro-scale spatiotemporal analysis, this paper empirically provides a comprehensive, yet granular, picture of collective human behaviors in cities. Using Seoul, South Korea as a case study site, it prioritizes the spatiotemporal context in order to mitigate uncertain contextual effects inherent in such forms of data-driven analysis. Instead of leaving the data re-grouping up to researcher’s arbitrary decision, this paper employs a functional principal component analysis (FPCA) to systematically transform a set of discrete data to a continuous functional form. This paper applies FPCA on 24-hour-based dataset of pedestrian traffic in Seoul in order to make a data-driven extraction of principal components that characterize the city’s unique patterns of urban vitality. Extracting principal components allows for less statistically obvious phenomena to be measured that would have otherwise been hidden within the data. This approach proved successful in capturing nighttime vitality patterns that are eclipsed by the overwhelming trend of daytime patterns. Additionally, this paper compares differences between regions and seasons to examine what the differences can tell about the definition of nighttime.

The Transformation of Reference Microbiology Methods and Surveillance for Salmonella With the Use of Whole Genome Sequencing in England and Wales.

The use of whole genome sequencing (WGS) as a method for supporting outbreak investigations, studying Salmonella microbial populations and improving understanding of pathogenicity has been well-described (1–3). However, performing WGS on a discrete dataset does not pose the same challenges as implementing WGS as a routine, reference microbiology service for public health surveillance. Challenges include translating WGS data into a useable format for laboratory reporting, clinical case management, Salmonella surveillance, and outbreak investigation as well as meeting the requirement to communicate that information in an understandable and universal language for clinical and public health action. Public Health England have been routinely sequencing all referred presumptive Salmonella isolates since 2014 which has transformed our approach to reference microbiology and surveillance. Here we describe an overview of the integrated methods for cross-disciplinary working, describe the challenges and provide a perspective on how WGS has impacted the laboratory and surveillance processes in England and Wales.

Harmonizing Cigar Survey Data Across Tobacco Centers of Regulatory Science, Center for Tobacco Products, and Population Assessment of Tobacco and Health Studies: The Cigar Collaborative Research Group.

IntroductionCigars are a popular tobacco product of choice for youth and young adults. Despite growing interest in cigar research, there are gaps in the available literature limiting an ability to set evidence-based policies. Too small research samples, the heterogeneity of types of cigars when asking a single question about use, makes analyzing data difficult. Given the Food and Drug Administration’s (FDA’s) authority granted in 2016 to regulate cigars, and its popularity, data to better understand use and preference for cigars will help FDA set appropriate regulatory policies.MethodsWe harmonized cigar survey data previously collected by five independent tobacco regulatory science survey research projects. Data supplying participants included three Tobacco Centers of Regulatory Science, one Center for Tobacco Products grantee, and data from Population Assessment of Tobacco and Health (PATH) study’s public use dataset.ResultsAnalyzing 92 data variables from across five studies, and applying a rigorous data harmonization protocol, we report findings on 24 key cigar use variables. The step by step protocol for harmonizing is presented. Selected findings showing strict reproducibility across all five studies reveal youth 17–19 years at highest risk for cigar initiation; relative reproducibility shows males more likely to try cigars than females but with significant differences in magnitude across studies; and areas of inconsistent reproducibility are revealed when evaluating brand preferences.ConclusionHarmonizing data from multiple sources fosters a broader view of the robustness and generalizability of survey data than that from a single source. These observations raise awareness to look for the highest degree of reproducibility among and across data sources to inform policy.ImplicationsHarmonizing data from discrete datasets provides insights into cigar initiation and use and is presented showing opportunities, challenges, and solutions. Comparing observational data from PATH and four independent research studies provides a best-practices approach and example of data synthesis for the tobacco research community. The dataset of five studies offers a look at the degree of confidence in analyzing harmonized survey results. Variable conclusions raise the need to strive for the highest degree of reproducibility, to best understand the behaviors of cigar users, and allow for the future development of the most effective interventions to alter tobacco use patterns.

Reduced Data Sets and Entropy-Based Discretization

Results of experiments on numerical data sets discretized using two methods—global versions of Equal Frequency per Interval and Equal Interval Width-are presented. Globalization of both methods is based on entropy. For discretized data sets left and right reducts were computed. For each discretized data set and two data sets, based, respectively, on left and right reducts, we applied ten-fold cross validation using the C4.5 decision tree generation system. Our main objective was to compare the quality of all three types of data sets in terms of an error rate. Additionally, we compared complexity of generated decision trees. We show that reduction of data sets may only increase the error rate and that the decision trees generated from reduced decision sets are not simpler than the decision trees generated from non-reduced data sets.

A Generalised Exponential-Lindley Mixture of Poisson Distribution

Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD.
 Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution.
 Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970).
 Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.

Bat algorithm and k-means techniques for classification performance improvement

This paper presents Bat Algorithm and K-Means techniques for classification performance improvement. The objective of this study is to investigate efficiency of Bat Algorithm in discrete dataset and to find the optimum feature in discrete dataset. In this study, one technique that comprise the discretization technique and feature selection technique have been proposed. Our contribution is in two process of classification: pre-processing and feature selection process. First, to proposed discretization techniques called as BkMD, where we hybrid Bat Algorithm technique and K-Means classifier. Second, to proposed BkMDFS as feature selection technique where Bat Algorithm is embed into BkMD. In order to evaluate our proposed techniques, 14 continuous dataset from various applications are used in experiment. From the experiment, results show that BkMDFS outperforms in most performance measures. Hence it shows that, Bat Algorithm have potential to be one of the discretization technique and feature selection technique.

Reconstructive utilisation and outcomes following mastectomy surgery in women with breast cancer treated in England.

Breast cancer usually necessitates breast-conserving surgery or mastectomy, which adversely affect appearance and wellbeing. Immediate reconstruction restores the breast mound but its availability and efficacy are uncertain. Two discrete datasets were used to evaluate mastectomies in England: Hospital Episode Statistics to measure overall activity and variation over time and by region and a national prospective audit to evaluate immediate reconstruction decision making, complication rates and patient-reported satisfaction with information, choice and outcomes. The 2005-08 Hospital Episode Statistics analyses identified 20% breast-conserving surgery reoperation rates nationally, frequently involving mastectomy. Rates were higher with in-situ disease present (30% vs 18%) and varied across NHS trusts (10th-90th centiles 12-30%). The 2008-09 national audit examined 18,216 women. The 19% immediate reconstruction rate varied regionally (9-43%), as did 2006-09 Hospital Episode Statistics data (8-32%). A total of 48% of women were offered immediate reconstruction, again varying regionally (24-75%). Offer likelihood fell with increasing age. National immediate reconstruction rates increased from 10% to 23% from 2000 to 2014, but regional variation persisted. Despite high care satisfaction, just 65% of mastectomy patients received the right amount of reconstructive information (90% for immediate reconstruction). Women from deprived areas experienced higher complication rates. Flap-based immediate reconstruction led to greater satisfaction with breast area appearance, emotional and sexual wellbeing and overall outcome than mastectomy; implant-only immediate reconstruction scored no better. Reconstruction is central to improving breast cancer outcomes. The differential outcomes and persistent regional inequalities identified should facilitate decision making, support improved access to all reconstructive options and inform the development of an optimal patient pathway.

A distribuição Half-Normal generalizada discreta: uma distribuição alternativa na análise de dados de contagem

Geralmente, dados que são obtidos por processos de contagem, estritamente discretos ou discretizados (provenientes de truncamentos e/ou arredondamentos), são analisados, sem exaustão, pelas distribuições Geométrica, Logarítmica, Poisson e Binomial negativa. Nos últimos anos um grande número de distribuições discretas vêm sendo propostas na literatura a partir da discretização de variáveis aleatórias contínuas. Muitos dos métodos de discretização preservam uma ou mais características da versão contínua, sendo que a proposta de Nakagawa e Osaki (1975) é a mais utilizada. Neste artigo, a partir dessa metodologia, a qual faz uso da função de sobrevivência, é proposta a versão discreta da distribuição Half-Normal generalizada contínua, introduzida na literatura por Cooray e Ananda (2008). Discute-se algumas de suas propriedades e via simulações Monte Carlo avalia-se o viés e a acurácia das estimativas obtidas pelo método da máxima verossimilhança e pelo método dos momentos. Alguns conjuntos de dados discretos da literatura são considerados para ilustrar a aplicabilidade da distribuição proposta.